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Book Information

Author(s): D. F. McGhee and R. H. Picard
Title: Cordes' two-parameter spectral representation theory
Additional book information: Pitman Research Notes in Mathematics Series, Volume 177, Longman Scientific and Technical, Harlow, United Kingdom and New York, 1988, 114 pp., $41.95. ISBN 0-470-21084-2

1.: F. M. Arscott, A treatment of the ellipsoidal wave equation, Proc. London. Math. Soc. (3) 9 (1959), 21-50. MR 104837
2.: F. M. Arscott, Two-parameter eigenvalue problems in differential equations, Proc. London. Math. Soc. (3) 14 (1964), 459-470. MR 165164
3.: F. V. Atkinson, Multiparameter spectral theory, Bull. Amer. Math. Soc. 74 (1968), 1-27. MR 220078
4.: F. V. Atkinson, Multiparameter eigenvalue problems: matrices and compact operators, Academic Press, New York and London, 1972. MR 451001
5.: P. J. Browne and B. D. Sleeman, Inverse multiparameter eigenvalue problems for matrices, Proc. Roy. Soc. Edinburgh Sect. (A) 100 (1985), 29-38. MR 801842
6.: R. D. Carmichael, Boundary value and expansion problems, Amer. J. Math. 43 (1921), 69-101; ibid. 43 (1921), 232-270; 44 (1922), 129-152.
7.: H. O. Cordes, Über die Spektralzerlegung von hypermaximalen Operatoren die durch Separation der Variablen zer fallen. I, Math. Ann. 128 (1954), 257-289; II, Math. Ann. (1955), 373-411. MR 66562
8.: A. Erdélyi, Higher transcendental functions, Bateman manuscript project vol. 3, McGraw-Hill, New York, Toronto, London, 1955.
9.: D. Hilbert, Grundzuge einer allgemeinsen Theorie der Linearen Integralgleichungen, Berlin, 1912.
10.: H. Isaev, Lectures on multiparameter spectral theory, Calgary, 1985.
11.: A. Källström and B. D. Sleeman, Solvability of a linear operator system, J. Math. Anal. Appl. 55 (1976), 785-793. MR 417833
12.: A. Källström and B. D. Sleeman, Joint spectra for commuting operators, Proc. Ed. Math. Soc. 28 (1985), 233-248. MR 806754
13.: F. Klein, Math. Ann. 18 (1881), p. 410, but see E. L. Ince, Ordinary differential equations, Dover, New York, 1956. MR 1510109
14.: F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), 116-229. MR 1503275
15.: A. J. Pell, Linear equations with two parameters, Trans. Amer. Math. Soc. 23 (1922), 198-211. MR 1501198
16.: B. P. Rynne, Multiparameter spectral theory and Taylor's joint spectrum in Hilbert space, Proc. Roy. Soc. Edinburgh Sect. (A) 31 (1988), 127-144. MR 930021
17.: B. P. Rynne, Uniform convergence of multiparameter eigenfunction expansions, J. Math. Anal. Appl. (to appear). MR 1050209
18.: B. D. Sleeman, Multiparameter spectral theory in Hilbert space, Research Notes in Mathematics, vol. 22, Pitman, London, 1978. MR 510467
19.: H. Volkmer, Multiparameter eigenvalue problems and expansion theorems, Lecture Notes in Math., vol. 1356, Springer-Verlag, Berlin and New York, 1988. MR 973644

Review Information:
Journal: Bull. Amer. Math. Soc. 22 (1990), 201-208.
DOI: 10.1090/S0273-0979-1990-15880-X
PII: S 0273-0979(1990)15880-X

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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